The peculiarities of the exchange interaction between the carrier spin and localized spin moments of magnetic ions near the semimetal-semiconductor transition have been studied in a semimagnetic quaternary solid solution system, Hg_1-x-yCd_xMn_ySe (x = 0.10, y = 0.02, E_g = 45 meV), by means of Shubnikov-de Haas oscillations. The measurements show that the exchange `constant' is actually a somewhat complicated function of energy gap E_g and electron concentration, which changes from negative values ( N₀ = -0.15 eV) at lower electron concentration to positive values ( N₀ = 0.28 eV) at higher electron concentration, values which are more typically associated with wide-gap semimagnetic semiconductors.